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- Homework Statement
- Consider a Hamiltonian H[s] that depends on a number of slowly varying parameters collectively called s(t). What is the effect on the Berry phase γn[C] for a given closed curve C, if H[s] is replaced with f[s] H[s], where f[s] is an arbitrary real numerical function of the s?

- Relevant Equations
- .

Homework Statement :

Consider a Hamiltonian

Homework Equations :

For any

Attempt at a Solution :

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Consider a Hamiltonian

**that depends on a number of slowly varying parameters collectively called***H[s ]***. What is the effect on the Berry phase***s(t)***for a given closed curve***γ*_{n}[C]**, if***C***is replaced with***H[s ]***, where***f[s ] H[s ]***is an arbitrary real numerical function of the***f[s ]***?***s*Homework Equations :

For any

**, we can find a complete orthonormal set of eigenstates***s**of***Φ**_{n}*with eigenvalues***H****:***E*_{n}(s)**HΦ**

(Φ._{n}= E_{n}Φ_{n}(Φ

_{n}, Φ_{m}) = δ_{nm}Attempt at a Solution :

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